A micromechanically manufacturable pressure sensor is discussed in EP 0 714 017 A1. The pressure sensor has a doped area of a substrate as the first electrode, and has a membrane layer as the second electrode, the membrane layer spanning a cavity which at least partially exposes the doped area of the substrate. Continuous recesses for exposing the cavity beneath the membrane layer are structured into the membrane layer, and are sealed off with the aid of a closure layer. Additional layers may optionally be applied to the closure layer.